Write balanced equations for each of the following nuclear reactions: $(\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{82}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\( (c) \){ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19} \mathrm{~F}$.

We have the following nuclear reaction: \[_{92}^{238}\mathrm{U}(\mathrm{n}, \gamma){ }^{239}\mathrm{U}\] Steps to balance the reaction: 1. Start with the original reaction: \(_{92}^{238}\mathrm{U}(\mathrm{n}, \gamma)\). 2. Add the neutron to the uranium nucleus: \[_{92}^{238}\mathrm{U} + _{0}^{1}\mathrm{n}\]. 3. Apply the conservation of atomic numbers: \(92 + 0 = 92\). 4. Apply the conservation of mass numbers: \(238 + 1 = 239\). 5. Write the balanced reaction as: \[_{92}^{238}\mathrm{U} + _{0}^{1}\mathrm{n} \rightarrow { }^{239}\mathrm{U}\]. The balanced equation for uranium capturing a neutron is: \[_{92}^{238}\mathrm{U}(\mathrm{n}, \gamma){ }^{239}\mathrm{U}\]

We have the following nuclear reaction: \[_{8}^{16}\mathrm{O}(\mathrm{p}, \alpha){ }^{13}\mathrm{N}\] Steps to balance the reaction: 1. Start with the original reaction: \(_{8}^{16}\mathrm{O}(\mathrm{p}, \alpha)\). 2. Add the proton to the oxygen nucleus: \[_{8}^{16}\mathrm{O} + _{1}^{1}\mathrm{p}\]. 3. Apply the conservation of atomic numbers: \(8 + 1 = 9\). 4. Apply the conservation of mass numbers: \(16 + 1 = 17\). 5. Write the balanced reaction as: \[_{8}^{16}\mathrm{O} + _{1}^{1}\mathrm{p} \rightarrow { }_{9}^{17}\mathrm{X} + _{2}^{4}\mathrm\nuclide{\alpha}\] 6. Identify the nuclide with atomic number 9: \(!_9\nuclide{F}\). 7. Finally, substitute the final term: \[_{8}^{16}\mathrm{O} + _{1}^{1}\mathrm{p} \rightarrow { }^{13}\mathrm{N} + _{2}^{4}\mathrm\nuclide{\alpha}\] The balanced equation for oxygen capturing a proton is: \[_{8}^{16}\mathrm{O}(\mathrm{p}, \alpha){ }^{13}\mathrm{N}\]

We have the following nuclear reaction: \[_{8}^{18}\mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19}\mathrm{F}\] Steps to balance the reaction: 1. Start with the original reaction: \(_{8}^{18}\mathrm{O}\left(\mathrm{n}, \beta^{-}\right)\). 2. Apply the conservation of atomic numbers: \(8 + 1 = 9\). 3. Apply the conservation of mass numbers: \(18 + 0 = 18\). 4. Write the balanced reaction as: \[_{8}^{18}\mathrm{O} \rightarrow { }_{9}^{18}\mathrm{X} + _{-1}^{0}\mathrm\nuclide{e}\] 5. Identify the nuclide with atomic number 9: \(!_9\nuclide{F}\). 6. Finally, substitute the final term: \[_{8}^{18}\mathrm{O} \rightarrow { }^{19}\mathrm{F} + _{-1}^{0}\mathrm\nuclide{e}\] The balanced equation for oxygen beta decay is: \[_{8}^{18}\mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19}\mathrm{F}\]